. The bar cannot expand,
since then the end points would depend on time. (Though you could
apparently still handle a length that grows as the square root of time
by a simple coordinate transform trick.)
First, the equation must be linear. (After all, the solution is found as an sum of simple solutions.)
The P.D.E. does not necessarily have to be a constant coefficient equation, but the coefficients cannot be too complicated. To be more precise, the second step in the procedure explained in the next section must work.
Further, the boundaries must be at constant values of the coordinates.
For example, for the heat conduction in a bar, the ends of the bar
must be at fixed locations x=0 and . The bar cannot expand,
since then the end points would depend on time. (Though you could
apparently still handle a length that grows as the square root of time
by a simple coordinate transform trick.)
11/15/00 0:04:29